It means that the bulb will work the best or glow most brightly if 15 watt of power is supplied to the appliance.
Power = Voltage * Current.
How much the current maybe or how much the voltage maybe but their product should equal to 15 for the proper functioning of the bulb
I f the power supplied is less than 15 watt then it will not glow dim not as bright as it was glowing at 15 watt but there will be no harm to the bulb
If we supply more than the 15 watt power the appliance may not work properly and it would be damaged and even it could be burst if a lot of power is supplied.
If the power is more than the rating then there would be more current or voltage.
Then according to Joule's law of heating Heat energy =Voltage * Current * Time. The heat produced will be more and the temperature may rise than the melting point of the filament of the bulb and the circuit may become open and then the complete bulb is a waste,
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Happy new Year!